Question: Solve for $x$ and $y$ using elimination. ${2x+y = 11}$ ${-3x+y = 6}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $-1$ ${-2x-y = -11}$ $-3x+y = 6$ Add the top and bottom equations together. $-5x = -5$ $\dfrac{-5x}{{-5}} = \dfrac{-5}{{-5}}$ ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {2x+y = 11}\thinspace$ to find $y$ ${2}{(1)}{ + y = 11}$ $2+y = 11$ $2{-2} + y = 11{-2}$ ${y = 9}$ You can also plug ${x = 1}$ into $\thinspace {-3x+y = 6}\thinspace$ and get the same answer for $y$ : ${-3}{(1)}{ + y = 6}$ ${y = 9}$